Velocity Distributions - Video Tutorials & Practice Problems
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Velocity Distributions represent probability distributions for a gas when examining their molar mass and temperature.
Velocity Distribution Curves
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concept
Velocity Distributions
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The shape of the Maxwell Boltzmann distribution curve is dependent on 2 factors: temperature and molecular weight. Alright, so for the first factor temperature, we have 2 curves. One's at 30 degrees Celsius and one's at 330 degrees Celsius. If we look at the apex or the very top of each curve we have our probable speed. Remember, the probable speed is where a majority of the gases will reside, the velocity in which they move. What we should see here is that for the curve at a higher temperature, the probable speed where a majority of them was moving looks like it's around 600 meters per second. But the probable speed for the curve at a lower temperature is only around 400 or so meters per second. So, what trend can we see here? Well, we can see here that as my temperature increases, the molecules moving at a higher velocity also increase. If we take a look here for the green curve we have just in this little portion here, this many gases moving at 800 meters per second or higher, not a great amount. But if we increase the temperature to 330 degrees Celsius, we see we have a bigger chunk of gases moving at 800 meters per second or greater. That's what happens. Increasing the temperature increase the velocity of many of the gases within each curve. So from this we can see as the temperature also increases the curve gets more broad and lower. So, more gases are able to move at a higher velocity. That's also what it's showing. For factor 2 we have molecular weight. So for factor 2 we have 4 curves for 4 gases. We have helium which is around 4 grams per mole, neon which is around 20 grams per mole, argon which is around 40 grams per mole or so, and finally xenon which is around a 131 grams per mole. What can we see here? Well, for Helium we can see that its probable speed is around 700 or so meters per second. And then for xenon, the one that wins the most, its probable speed is only around a 100 or so meters per second. So, what trend can we make here? Well, the trend we see here is that as the molecular weight increases, molecules moving at a higher velocity decreases. So if you weigh more as a gas it's harder for you to propel yourself, move yourself, and that's what we're seeing. Helium weighs the least so it's easier for it to move faster around. Now, as a result of this also in terms of molecular weight, we can see that helium which weighs the least also has the most broad curve. So, we can say here as the molecular weight decreases the curve gets more broad and lower, meaning more gases are able to get to a certain type of velocity as everyone else. Right? So these are the trends we need to realize when it comes to gaseous molecules when we factor in the, effects of temperature and molecular weight on their velocities.
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example
Velocity Distributions Example 1
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For this example question it says, the graph illustrated below shows the distribution of molecular velocities. How many of the following statements is are true? Alright. So we have let's take a look. We have 3 curves within this graph. We have the red curve, the blue curve, and the green one. Here we can see that on our y axis we have the number of molecules, and then on our x axis we have our velocities. So for 1, at a given temperature curve a is measured at the highest temperature. So curve a is the red one. Remember, we said that the higher your temperature goes then the more broad, the more broad the curve gets. The most broad one is the green curve, curve c. So it would have the highest temperature. Next, for a given gas sample, curve c represents gas molecules with the smallest molar mass. Well, we said that the lower your molar mass, then the also more broad your curve gets. Since curve c is the most broad, it makes sense that it would have the smallest molar mass. So this is true. And then here, we just said that curve c has the highest, smallest molar mass, so it couldn't have the highest molar mass as well. And then for 4, for a given gas sample, the more narrow the velocity distribution, temperature. So remember, we said the higher your temperature gets the more broad the curve becomes. So if we do the opposite, the lower your temperature gets then the more narrow your curve will become. We'd say here that curve a is the most narrow, therefore it would be at the lowest temperature. So this statement here is true. The more narrow the velocity distribution in terms of the curve, then the lower the temperature is. So out of the 4 statements 2 of them are true. This makes option c the correct choice.